The receiver should be placed
at the **focus** of the parabolic dish for best
reception, because the incoming signal will be concentrated at
the focus.

We place the vertex of the
parabola at the origin (for convenience) and use the equation of
the parabola to get the focal distance (*p*) and hence the
required point.

In general, the equation for a parabola with vertical axis is

`x^2 = 4py.`

We can see that the parabola passes through the point `(6, 2)`.

Substituting, we have:

`(6)^2 = 4p(2)`

So `p = 36/8 = 4.5`

So we need to place the receiver 4.5 metres from the vertex, along the axis of symmetry of the parabola.

The equation of the parabola is:

`x^2 = 18y `

That is

`y = x^2 /18`

Easy to understand math videos:

MathTutorDVD.com